| Description |
1 online resource (xi, 428 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 42
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World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 42.
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| Bibliography |
Includes bibliographical references and index. |
| Contents |
1. Coupled nonlinear oscillators. 1.1. The role of synchronization. 1.2. Synchronization measures. 1.3. Mode-locking of endogenous economic cycles -- 2. Transverse stability of coupled maps. 2.1. Riddling, bubbling, and on-off intermittency. 2.2. Weak stability of the synchronized chaotic state. 2.3. Formation of riddled basins of attraction. 2.4. Destabilization of low-periodic orbits. 2.5. Different riddling scenarios. 2.6. Intermingled basins of attraction. 2.7. Partial synchronization for three coupled maps -- 3. Unfolding the riddling bifurcation. 3.1. Locally and globally riddled basins of attraction. 3.2. Conditions for soft and hard riddling. 3.3. Example of a soft riddling bifurcation. 3.4. Example of a hard riddling bifurcation. 3.5. Destabilization scenario for a = a[symbol]. 3.6. Coupled intermittency-III maps. 3.7. The contact bifurcation. 3.8. Conclusions -- 4. Time-continuous systems. 4.1. Two coupled Rossler oscillators. 4.2. Transverse destabilization of low-periodic orbits. 4.3. Riddled basins. 4.4. Bifurcation scenarios for asynchronous cycles. 4.5. The role of a small parameter mismatch. 4.6. Influence of asymmetries in the coupled system. 4.7. Transverse stability of the equilibrium point. 4.8. Partial synchronization of coupled oscillators. 4.9. Clustering in a system of four coupled oscillators. 4.10. Arrays of coupled Rossler oscillators -- 5. Coupled pancreatic cells. 5.1. The insulin producing beta-cells. 5.2. The bursting cell model. 5.3. Bifurcation diagrams for the cell model. 5.4. Coupled chaotically spiking cells. 5.5. Locally riddled basins of attraction. 5.6. Globally riddled basins of attraction. 5.7. Effects of cell inhomogeneities -- 6. Chaotic phase synchronization. 6.1. Signatures of phase synchronization. 6.2. Bifurcational analysis. 6.3. Role of multistability. 6.4. Mapping approach to multistability. 6.5. Suppression of the natural dynamics. 6.6. Chaotic hierarchy in high dimensions. 6.7. A route to high-order chaos -- 7. Population dynamic systems. 7.1. A system of cascaded microbiological reactors. 7.2. The microbiological oscillator. 7.3. Nonautonomous single-pool system. 7.4. Cascaded two-pool system. 7.5. Homoclinic synchronization mechanism. 7.6. One-dimensional array of population pools. 7.7. Conclusions -- 8. Clustering of globally coupled maps. 8.1. Ensembles of coupled chaotic oscillators. 8.2. The transcritical riddling bifurcation. 8.3. Global dynamics after a transcritical riddling. 8.4. Riddling and blowout scenarios. 8.5. Influence of a parameter mismatch. 8.6. Stability of K-cluster states. 8.7. Desynchronization of the coherent chaotic state. 8.8. Formation of nearly symmetric clusters. 8.9. Transverse stability of chaotic clusters. 8.10. Strongly asymmetric two-cluster dynamics -- 9. Interacting nephrons. 9.1. Kidney pressure and flow regulation. 9.2. Single-nephron model. 9.3. Bifurcation structure of the single-nephron model. 9.4. Coupled nephrons. 9.5. Experimental results. 9.6. Phase multistability. 9.7. Transition to synchronous chaotic behavior -- 10. Coherence resonance oscillators. 10.1. But what about the noise? 10.2. Coherence resonance. 10.3. Mutual synchronization. 10.4. Forced synchronization. 10.5. Clustering of noise-induced oscillations. |
| Summary |
Interacting chaotic oscillators are of interest in many areas of physics, biology, and engineering. In the biological sciences, for instance, one of the challenging problems is to understand how a group of cells or functional units, each displaying complicated nonlinear dynamic phenomena, can interact with one another to produce a coherent response on a higher organizational level. This book is a guide to the fascinating new concept of chaotic synchronization. The topics covered range from transverse stability and riddled basins of attraction in a system of two coupled logistic maps over partial synchronization and clustering in systems of many chaotic oscillators, to noise-induced synchronization of coherence resonance oscillators. Other topics treated in the book are on-off intermittency and the role of the absorbing and mixed absorbing areas, periodic orbit threshold theory, the influence of a small parameter mismatch, and different mechanisms for chaotic phase synchronization. The biological examples include synchronization of the bursting behavior of coupled insulin-producing beta cells, chaotic phase synchronization in the pressure and flow regulation of neighboring functional units of the kidney, and homoclinic transitions to phase synchronization in microbiological reactors. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Chaotic behavior in systems.
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Chaotic behavior in systems. |
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Synchronization.
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Synchronization. |
| Genre/Form |
Electronic books.
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| Added Author |
Maĭstrenko, I͡U. L. (I͡Uriĭ Leonidovich)
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Postnov, Dmitry.
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| Other Form: |
Print version: Mosekilde, Erik. Chaotic synchronization. Singapore ; River Edge, NJ : World Scientific, ©2002 9810247893 9789810247898 (DLC) 2002511018 (OCoLC)50809016 |
| ISBN |
9789812778260 (electronic book) |
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9812778268 (electronic book) |
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